[r-t] 23-spliced

[Richard Smith]

Philip Earis wrote:

> One thing I've wondered for a while is whether any compositions of
> 23-spliced treble-dodging major exist that are in whole courses.  I'm not
> looking for trivial Derwent variants here (and yes, I have seen Colin
> Wylde's 24-spliced). Any ideas much appreciated.

I suppose I should reply to this sooner rather than later.

Back on the 8th Dec, Phil provided me with a base
composition for 2nds place methods with only calls at Home
(i.e. every 7 leads).  Necessarily, it uses more than one
type of call -- both 4ths and 6ths place bobs.

  5152 TD Major

  H        23456
  --------------
  x ) A    42635
  - )      64235
  A        52643
  -        65243
  3A       53462
  3x       62345
  4A       34256
  -        23456
  --------------

  - = 14; x = 16

This is true for a method with B falseness such as
Yorkshire.

My first attempt at fitting methods to this was to start
with 23 courses of Yorkshire and gradually perturb the
methods until I had something more interesting.  Quite
quickly my program produced its first set of 23 methods for
this composition.  (Methods in order of appearance, so m0 is
the first course, m1, the second, etc.)

  m0 = &-36-1.56-2.3-2-1.34-6.7;
  m1 = &-56-1.56-5.6.34-34.1-6-3;
  m2 = &-3-4-2-36-34-3.6-56.7;
  m3 = &-56-4.5-56.3.2-34.1-56-1;
  m4 = &-36-1-2-3.2-4.5.2-2.5;
  m5 = &-36-4.56-2.3.2-2.5-6-5;
  m6 = &56-56.1.56-2.3.2-2.5-6-7;
  m7 = &34-34.1.56-56.3-34-3-6-7;
  m8 = &56-3.4.5-2.36-2-1.34-56.7;
  m9 = &-56-1.56-2.3-2-1-56-1;
  m10 = &-36-1-2-6.34-34.5-56-1;
  m11 = &-36-1.56-2.3.2-4.3.4-6.7;
  m12 = &34-56.1-56-36-34-3.6-56.3;
  m13 = &-34-1.56-5.36-34-1.34-36.7;
  m14 = &34-34.1.56-5.36-34-5.6-4.7;
  m15 = &-56-1.56-5.6-4-1.36-2.3;
  m16 = &-36-4.56-2.36-4-5.34-4.7;
  m17 = &-56-4-5-1-2-5.34-34.1;
  m18 = &-36-4.56-2.3.2-2.5.6-2.7;
  m19 = &-34-1-56-3-34-5.34-36.7;
  m20 = &-5-1-5-3.2-2.5.34-34.7;
  m21 = &-34-4-2-6-2-3-36-7;
  m22 = &-36-1.56-56.3.2-2.5.4-2.5;

This came as a surprise to me.  Although the methods are not
a particularly inspiring selection, I was surprised by
little evidence remained of the Yorkshire that I used to
seed the algorithm (for instance, none of the methods begin
-3-).

After some further tinkering, I managed to remove all the
delight methods (the majority in the previous composition),
change the balance of methods in favour of the less static
ones (which I did by decreasing the likelyhood of 34 and 56
place notations), and increase the proportion of right-place
methods.

  m0 = &-3-6-5-36-34-5-6-5;
  m1 = &-5-4-56-6-4-5-2-5;  // [Heydour]
  m2 = &5-5.6.5-2.3-2-5-4-1;
  m3 = &-3-4-56-6-2-5-4-5;  // [Lessness]
  m4 = &36-5.4-5-6-2-5-36-5;
  m5 = &-5-4-2-3-34-5-4-3;
  m6 = &-3-6-56-3-34-5.36-56.3;
  m7 = &-5-6-5-6-2-5-56-5;
  m8 = &3-5.6.5-2.3.2-2.3-2-3;
  m9 = &-56-6-5-3.4-2.3.2-34.5;
  m10 = &-34-4-5-3-4-5-34-1;
  m11 = &-34-4-2-6-2-5-2-7;
  m12 = &34-36.4.5-2.3.2-4.5.6-6.7;
  m13 = &-34-4-2-3-4-5-36-1;
  m14 = &-34-4-5-6-2-3-6-3;  // [Xyster]
  m15 = &-34-4-5-3-2-5-6-3;
  m16 = &-5-6-5-3-2-5-56-3;  // [Helston]
  m17 = &-5-4-2-3-2-5-36-5;
  m18 = &-5-4-56-36-2-5-2-5;
  m19 = &-5-4-5-6-2-5-2-1;  // [Aspenden]
  m20 = &-5-4-5-6-4-5-6-7;
  m21 = &-5-4-56-3-2-3-56-3;
  m22 = &-5-4-5-6-2-3-6-1;

I response to some suggestions from Phil, I then looked at
some specific questions.  First, can it be done with just
right place methods?  The answer is yes:

  m0 = &-5-4-2-36-2-3-56-1;  // [Bearwood]
  m1 = &-3-6-5-36-2-3-6-1;
  m2 = &-3-6-2-6-2-5-36-7;
  m3 = &-5-4-2-3-4-5-36-3;
  m4 = &-36-4-5-3-4-3-34-5;
  m5 = &-36-4-2-36-2-5-4-1;
  m6 = &-56-6-5-3-2-5-56-5;
  m7 = &-3-6-2-6-4-3-34-1;
  m8 = &-3-4-2-6-2-5-4-7;  // [Truro]
  m9 = &-5-4-5-3-4-5-6-5;
  m10 = &-5-4-5-6-4-3-2-5;
  m11 = &-5-4-2-3-4-3-2-5;
  m12 = &-34-4-56-6-2-3-4-1;
  m13 = &-34-6-2-3-4-5-4-1;
  m14 = &-34-6-2-3-2-5-56-1;
  m15 = &-34-4-56-36-2-5-2-5;
  m16 = &-5-4-2-3-2-3-2-3;
  m17 = &-5-6-2-3-2-5-4-5;  // [Runnymede]
  m18 = &-3-6-2-3-4-5-56-3;
  m19 = &-5-4-2-3-4-3-6-1;  // [Wordsworth]
  m20 = &-5-4-2-36-34-3-34-5;
  m21 = &-3-6-5-6-2-3-4-3;
  m22 = &-5-4-5-36-2-3-34-3;

Second, can it be done only with named methods?  Yes, I
could only do this by allowing double changes.

  m0 = &-3-4-2-6-4-5-2-3;  // [Wombourn]
  m1 = &-3-4-256-6-34-45-4-5;  // [Grampian]
  m2 = &-3-4-5-6-34-3-34-5;  // [Dorking]
  m3 = &-3-4-2-3-4-25-6-5;  // [Chorley]
  m4 = &-3-4-5-6-4-5-236-7;  // [Gainsborough]
  m5 = &-3-4-5-6-4-25-36-7;  // [Nailstone]
  m6 = &-3-4-5-6-2-5-6-5;  // [Whitminster]
  m7 = &-3-4-2-6-4-45-456-3;  // [Stranton]
  m8 = &-3-4-56-6-2-3-4-3;  // [Worthington]
  m9 = &-3-4-56-6-2-45-6-5;  // [Colmore]
  m10 = &-3-4-56-6-2-5-4-5;  // [Lessness]
  m11 = &-3-4-25-6-4-3-256-7;  // [Jonah]
  m12 = &-3-4-5-6-4-5-456-3;  // [Maldon]
  m13 = &-3-4-25-3-4-5-6-3;  // [Goulburn]
  m14 = &-3-4-2-6-2-45-4-1;  // [Majestic]
  m15 = &-3-4-56-6-4-45-36-5;  // [Swineshead]
  m16 = &-3-4-2-6-4-5-6-5;  // [Axminster]
  m17 = &-3-4-5-6-234-5-2-1;  // [Brassica Oleracea Gemmifera]
  m18 = &-3-4-2-6-2-45-2-7;  // [Orpington]
  m19 = &-3-4-2-3-234-345-6-7;  // [Trelawney]
  m20 = &-3-4-5-6-4-25-236-7;  // [Johannesburg]
  m21 = &-3-4-5-6-34-3-6-1;  // [Hinton]
  m22 = &-3-4-5-6-4-45-56-3;  // [Itchy Park]

Sadly, all the methods start -3-4.  Although I tried quite
hard to find a more varied composition, I couldn't produce
one.

Obviously most of these compositions are really just "proofs
of concept" -- I think quite a bit more work would be needed
to produce something that anyone would actually want to
ring.  But it's certainly possible.

Richard